Final answer:
Booker T. Washington did not mention the specific entry examination he took, but he attended Hampton Institute and was recommended to become the first leader of Tuskegee Normal and Industrial Institute. This implies that Washington underwent an interview or a selection process for these institutions.
Step-by-step explanation:
In 'My Struggle for Education' by Booker T. Washington, the author did not mention the specific entry examination he took. However, it is known that Washington attended Hampton Institute and was recommended by the president to become the first leader of Tuskegee Normal and Industrial Institute. So, it can be inferred that Washington underwent an interview or a selection process to be chosen for these educational institutions.